A very quick summary:
The Fourier series was developed to solve the heat equation, a problem in physics regarding heat diffusion.
Mathematically, the Fourier series breaks down functions into infinite sums of sines and cosines, which given the potentially chaotic nature of the original function, is a powerful way to understand and analyze an arbitrary function by using trigonometry, a well-understood mathematical concept.
In neuroscience, the related concept of the Fast Fourier Transform is oftentimes used when processing EEG and other kinds of psychophysiological data.
It's really hard to fully express how much I'm amazed by this development of a mathematical tool for solving a physics problem, which finds its applications in neuroscience hundreds of years later.
So, as I was learning math and getting involved in neuroscience research, I kept asking myself:
"Yea, this math concept is very abstract, but will it find its use in neuroscience in some way?"
I will keep asking myself this question, and hopefully it doesn't take hundreds of years for me to find out.